By using expressions for the reduced matrix elements of the generators of R(5) which were obtained by considering R(5) ↓ SU(2)⊗ SU(2) reduction, a method for directly evaluating analytical expressions for the R(3) scalar shift-operator O0l eigenvalues is discussed.

In order to obtaining additional label-generating operators for the classification of octupolephonon states, a set of shift operators Pkl (k = ± 5,…, 5) in the G2 group and Okl (k = ± 3,…, 3) in the R(7) group, is constructed. Expressions connecting R(3) scalar and non-scalar products of...

O(3) shift operators O±kl (k = 0, 1, 2) constructed by means of SU(3) generators, can be combined into bilinear forms which are non-scalar with respect to the O(3) subgroup. These are shown to satisfy simple relations which are of importance in deriving eigenvalue expressions of the scalar...